Monotonicity  properties of systems have proven to be very powerful and useful for analyzing and controlling complex systems [1]}, [2]}. Building upon this idea, it  was shown that certain nonmonotone systems can be lifted to higher dimensional monotone systems that can be potentially used to deduce critical information about the original system (see e.g., [3]}, [4]}, [5]}) by decomposing the system dynamics into increasing and decreasing components. Systems that are decomposable in this manner are called  mixed-monotone and are significantly more general than the class of monotone systems.
